Following Leaver [1]} we obtain a continued fraction:
\(\beta _1^{(4)} &=& \frac{\alpha _1^{(4)} \gamma _{2}^{(4)}}{\beta _{2}^{(4)}-\frac{\alpha _{2}^{(4)}\gamma _{3}^{(4)}}{\beta _{3}^{(4)} - \cdots }} \nonumber \\&=& \frac{\alpha _1^{(4)}\gamma _{2}^{(4)}}{\beta _{2}^{(4)}-}\frac{\alpha _{2}^{(4)}\gamma _{3}^{(4)}}{\beta _{3}^{(4)} -}\frac{\alpha _{3}^{(4)}\gamma _{4}^{(4)}}{\beta _{4}^{(4)} -}\cdots \) 
